论文标题
非稳定的费尔米管极限形状
Non-probabilistic fermionic limit shapes
论文作者
论文摘要
我们在虚构的时间内研究了一个不均匀的邻居和最初的邻居跳跃术语，以一类不均匀的边界条件研究了一个不变的自由费式模型。已知该模型在没有下一个最新的邻居扰动的情况下会产生限制形状和北极曲线。事实证明，被认为的扰动并不总是积极的，也就是说，相应的统计机械模型并不总是具有正玻尔兹曼的重量。我们研究了这种非阳性扰动如何影响密度曲线。我们发现，在某些地区，负符号的效果被抑制，并重新归一致至零。但是，根据边界条件的不同，新的“疯狂区域”出现了，其中负迹象散发出来，而费米子的密度不再以$ [0,1] $为单位。我们为这种行为提供了一个简单的直觉，并在晶格上和缩放限制上精确地计算密度曲线。
We study a translational invariant free fermions model in imaginary time, with nearest neighbor and next-nearest neighbor hopping terms, for a class of inhomogeneous boundary conditions. This model is known to give rise to limit shapes and arctic curves, in the absence of the next-nearest neighbor perturbation. The perturbation considered turns out to not be always positive, that is, the corresponding statistical mechanical model does not always have positive Boltzmann weights. We investigate how the density profile is affected by this nonpositive perturbation. We find that in some regions, the effects of the negative signs are suppressed, and renormalize to zero. However, depending on boundary conditions, new "crazy regions" emerge, in which minus signs proliferate, and the density of fermions is not in $[0,1]$ anymore. We provide a simple intuition for such behavior, and compute exactly the density profile both on the lattice and in the scaling limit.
